Derivation — Domains of Attraction and the GEV Limit

The previous lesson stated the Fisher–Tippett–Gnedenko theorem and tabulated which distributions fall into which extreme value type. This note proves the Fréchet MDA characterisation (Gnedenko's Theorem 5.8), explains slowly and regularly varying functions, and verifies the MDA type for the normal, Student-$t$, Pareto, and exponential distributions. The derivations are the formal engine behind the table in the parent lesson — understanding them makes it possible to check whether any new distribution is in the Fréchet class without looking it up.